Chem reaction engineering example questions PDF

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Some useful Chemical Reaction engineering questions for practice...

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Contents Example problems: stirred batch reactors....................................................................................... 2 Example problems: continuous stirred tank reactors ...................................................................... 5 Example problems: tubular reactors ............................................................................................... 7 Example problems: semi-batch reactors ......................................................................................... 9 Example problem: combinations of different reactor types.......................................................... 10 Practice problems ......................................................................................................................... 11 Bibliography ................................................................................................................................. 15 Appendix – Tables........................................................................................................................ 16

Examples and exercise problems – Reactors The following examples and exercises are grouped by the generally accepted reactor categories. Depending on the mode of operation, a tank reactor (typically stirred, perfect mixing in ideal cases) can be classified as: 

batch (no input or output during the reaction),



semi-batch (at least one component is added or removed either continuously or after a delay),



continuous (the ideal version, assuming perfect mixing, is the so-called continuous stirred tank reactor or CSTR).

The other group of reactors comprises (continuous) tubular reactors. Ideal tubular reactors exhibit plug flow. Based on heat transfer, reactors can be classified as: 

isothermal,



adiabatic,



polytropic (a cooled or heated reactor in which temperature varies over time or by location). Strictly speaking, most real reactors belong in this category.

Based on the number of phases, reactors/reactions can categorized as: 

single phase, i.e. homogeneous (gas, liquid, supercritical fluid),



two or more phases, i.e. heterogeneous (gas–liquid, gas–solid, liquid–solid, liquid–liquid, gas– liquid–solid etc.)

All examples and exercises are grouped by reactor type and involve only homogeneous reactions. Example problems: stirred batch reactors Example 1: Isothermal batch reactor, first-order reaction An isomerization reaction is carried out in a batch reactor. The reaction is first-order, both isomers are liquids with a density of 900 kg/m3 at 163 °C. The reactor is filled in 10 minutes and emptied in 12 minutes. During the 14 minutes required to heat up the reactor, the reaction is negligible, it can be assumed to begin only when 163 °C is reached. 900 t of product must be synthesized in 7000 hours of operation per year. Conversion is 97%. What is the required volume of the stirred batch reactor operated isothermally at 163 °C? The reaction rate coefficient is 0,8 1/h. V  0,74 m 3

Example 2: Isothermal batch reactor, second-order reaction The reaction A+2BC+2D is carried out in an isothermal, perfectly stirred batch reactor at 80 °C. The reaction rate can be described as second-order, i.e. r  k  cA  cB , where k  0,058 m 3 /(kmol min) . At 80 °C, 200 kg of material A (MA=90 g/mol) and 400 kg of material B (MB=90 g/mol) is measured into the reactor. At this point, the (liquid) reaction mixture has a volume of 850 dm3. The reaction does not change the volume. What conversion can be achieved in 35 minutes? X  0,914

2

Example 3: Isothermal, second-order reaction The reaction A+BC+D is carried out at 80 °C in an isothermal, perfectly stirred tank reactor. The reaction rate can be described as second-order, where k  0,058 m 3/(kmol min) . At 80 °C, 240 kg of material A (MA=60 g/mol) and 400 kg of material B (MB=90 g/mol) is measured into the stirred tank. At this point, the volume of the (liquid) reaction mixture is 900 dm3. The reaction does not change the volume. How much time is required to reach 95% conversion? Solution t  9,96 min

Example 4: Isothermal, pseudo-first-order reaction The hydrolysis of acetic anhydride in a dilute aqueous solution appears to be a first-order reaction: (CH3CO)2O+H2O →2CH3COOH A+B →2C In a dilute solution (cA < 0.2 mol/dm3) the reaction rate coefficient can be calculated with the following equation: k  9,2335 10 6  e

5335 T

1 . min

If 200 kg/h acetic acid must be produced at 35 °C with an initial anhydride concentration of 0.2 mol/dm3, what is the required volume of the reactor? Servicing time is 15 min per batch. The desired conversion is 98%.

V  4,25 m 3 Example 5: Isothermal, equilibrium reaction Propanoic acid is synthesized in the following reaction: C2H5COONa +HCl

k1   

C2H5COOH + NaCl

k 1

In aqueous solution, the reaction is reversible and second-order. A series of isothermal experiments with 2.7 mol/dm3 initial concentration were performed in a laboratory-scale batch reactor to determine the reaction rate coefficient. A sample was taken from the reactor every 10 minutes, and the conversion of sodium propanoate was determined: time

(min)

0

10

20

30

50

∞

Conversion

(%)

0

39

55

64

72,5

80

Based on the data in the table, design an isothermal batch reactor do produce 1360 kg/h propanoic acid. Servicing time (loading, heating, cooling and emptying) is 45 minutes per batch. Since the equilibrium conversion of sodium propanoate is 80%, use an operating conversion of 75%. Initial concentrations in the industrial reactor are 323 kg/m3 sodium propanoate and 123.4 kg/m3 hydrochloric acid (100% HCl). The density of the reaction mixture is constant, 1200 kg/m3.

V  11,8 m3 Example 6: Isothermal batch reactor, equilibrium reaction In an equilibrium reaction, ethyl acetate is synthesized from ethanol and acetic acid in an isothermal batch reactor at 100 °C, in the presence of hydrochloric acid as catalyst. An aqueous solution containing 23 m/m% acetic acid, 46 m/m% ethanol and no ethyl acetate is measured into the reactor. 3

The average density of the solution is 1020 kg/m3. When the reaction is stopped, conversion is 35%. The value of the equilibrium constant Kc is 2.39. The reaction rate coefficient k1 is 7.93·106 m3/kmol·s. From the start of the reaction, how much time is required to reach the desired conversion? 2.1 hours. Example 7: Isothermal gas phase reaction, changing number of moles Determine the reaction rate coefficient for the gas phase decomposition of dimethyl ether, based on the pressure change measured in a constant volume reactor! The reaction is first-order and irreversible: (CH3)2O →CH4 +H2 + CO The measurement was carried out by filling the reactor with pure dimethyl ether at time t = 0 and measuring the increase in pressure at a constant temperature of 504 °C. time

(s)

390

777

1195

3155

∞

pressure change

(mmHg)

96

176

250

476

619

k = 0,0005 1/s. Example 8: Adiabatic reaction, batch reactor, first-order reaction An isomerization reaction is carried out in a batch reactor. The reaction is first-order, both isomers are liquids and have a density of 900 kg/m3 (density can be considered to be constant). The reaction rate coefficient is 0.8 h-1 at 163 °C. The reaction has an enthalpy of -347.5 J/g and an activation energy of 1.21·105 J/mol. The molar mass of the material is 250 g/mol. Loading and emptying the reactor takes 10 and 12 minutes, respectively. During the 14 minutes required to heat up the reactor, the reaction is negligible, it can be assumed to begin only when 163 °C is reached. 900 t of product must be synthesized in 7000 operating hours per year. Conversion is 97%. What is the required volume of the stirred tank reactor operated adiabatically?

V  0,11 m3 Example 9: Adiabatic, second-order reaction A Diels–Alder reaction is carried out in an adiabatic batch reactor. Symbolically: A+B → C Benzene is used for solvent, the initial concentration of the components is 0.15 kmol/m3. The initial temperature of the reaction mixture is 25 °C. How much time is required to reach 50% conversion? Data: k  3,162310 6  e

H R  72,8

5834 T

m3 kmol s

kJ . mol

The density and heat capacity of the solution can be considered to be constant. Since the solutions are dilute, the data for benzene can be used for calculations: cp = 1,75 kJ/(kg·K), ρ = 880 kg/m3 10 min.

4

Example problems: continuous stirred tank reactors Example 10: Isothermal continuous stirred tank reactor, irreversible reaction The hydrolysis of acetic anhydride is carried in a continuous stirred tank reactor at 25°C. The reaction is pseudo-first-order. The feed stream (0.6 m3/h) is a 0.9 kmol/m3 solution of acetic anhydride. The reaction rate coefficient is 0.0806 min-1. The desired conversion is 97%. Calculate the required volume of the reactor! Solution V  4 m3

Example 11: Isothermal continuous tank reactor, irreversible reaction The laboratory synthesis of hexamethylene tetramine (C) from aqueous solutions of ammonia (Aand formaldehyde (B) proceeds at 36 °C, in a continuous stirred tank reactor (CSTR). The mixing can be considered as ideal. The reactor has a useful volume of 490 cm3. The density of the reaction mixture does not change. The feed streams enter the reactor via two separate pipes at a rate of 1.5 cm3/s each. Stream A contains 4.06 mol/dm3 of ammonia, stream B contains 6,32 mol/dm3 formaldehyde. The consumption rate of A can be calculated with the formula rA  k  c A  c 2B . The reaction rate constant is given by k  1,42 103 e



3090 T

dm 6 , where T denotes the absolute temperature. The reaction equation mol 2 s

is as follows: 4 NH3+6 HCHO→(CH2)6N4+6 H2O Calculate the outlet concentrations and the conversion at steady state! Solution X = 0,821, cB = 0,66 mol/dm3, cC = 0,417 mol/dm3. Example 12: Isothermal, irreversible first-order reaction An A→B reaction which is first-order with respect to A is carried out in an isothermal, continuously stirred tank reactor, in dilute solution. The reaction rate constant can be calculated with the Arrhenius equation, and at 150 °C k = 15.53 h-1. The feed concentration of component A is 0.250 mol/dm3, at a rate of 0.35 dm3/min. E = 4752.6 J/mol. Calculate the conversion for the reaction a) carried out at 20 °C, b) carried out at 150 °C. Solution

X  0,67 X  0,787 . Example 13: Isothermal equilibrium reaction An equilibrium reaction of the type A+B

k1    k 1

C+D is carried out in a 0.12 m3 continuous stirred tank

reactor. The desired conversion is 75 %. Feed streams are equal and contain only one component each. Stream A contains 2.8 mol/dm3 of component A, stream B contains 1.6 mol/dm3 of component B. The value of k1 is 7 dm3/(mol·min), the value of k-1 is 3 dm3/(mol·min). What is the required feed rate? Solution 5

V dm3 V A  V B   4 min 2

Example 14: Adiabatic reaction, first-order irreversible reaction An irreversible A→B reaction is carried out in a perfectly stirred continuous adiabatic reactor. the reaction enthalpy is –12800 kJ/kmol, the reaction rate constant can be calculated with the formula 8.41·104·e-49200/RT (s-1). The mixture has an average specific heat capacity of 2440 J/(kg·K) and a density of 800 kg/m3. The feed concentration of A is 12 kmol/m3. The reaction enthalpy and the specific heat capacity of the materials do not depend on the temperature. a) Calculate the conversion and the reactor temperature, if the initial mixture is fed into a reactor with 3.9 m3 useful volume at 303 K, at a rate of 0.006 m3/s! b) Calculate the conversion and the reactor temperature, if the initial mixture is fed into a reactor with 3.25 m3 useful volume at 283 K! The average residence time is kept equal to that in part a). Solution Example 15: Tank reactor cascade, pseudo-first-order reaction The hydrolysis of acetic anhydride (a pseudo-first-order reaction) is carried out in a cascade of four stirred tank reactors of equal volume. The consecutive tanks are operated at progressively higher temperatures (10 °C, 15 °C, 25 °C, 40 °C). The reaction rate constant can be determined from the Arrhenius equation. The value of the preexponential factor is 22655200 min-1, the activation energy is 46311.15 J/mol. The desired conversion is 91%. The feed rate is 0.1 m3/min. Calculate the volume of the reactors. Solution

V  V  t  0,1

m3  5 min  0,5 m3 min

Example 16: Cooled tank reactor A liquid phase, irreversible, first-order reaction is carried out in a continuous stirred tank reactor. The feed temperature is 293 K, the average residence time is 1200 s, the maximal adiabatic temperature increase is 165.9 K, the value of the preexponential factor is 32500 s-1, the activation energy is 45.66 kJ/mol, the cooling parameter is 1,482, the feed concentration is 8 kmol/m3. determine the stationary operating point of the reactor for average coolant temperatures of 273.45 K and 289.2 K. 6

Check if the criteria of dynamic stability are satisfied for the given operating parameters. Solution Example 17: Tank reactor cascade, second-order irreversible reaction A second-order irreversible reaction of the form A+BC+D is carried out in a cascade of 3 tank reactors with 2 m3 useful volume in each reactor. 333 kg/h of A and 111 kg/h of B are fed into the first reactor, and an additional 148 kg/h of B is fed into the second reactor along with the stream arriving from the first reactor. The molar masses of the components are: M A = 222 g/mol, MB = 74 g/mol, MC = 278 g/mol, M D = 18 g/mol. The feed streams are perfectly mixed as soon as they are fed into the reactors, each reactor can be regarded as a perfectly mixed tank reactor. The density of the reaction mixture is 1058 kg/m3 and remains constant during the reaction. Each element in the cascade operates under isothermal conditions at 40 °C. The reaction rate constant is 1.25·10-3 m3/(kmol·min). a) How many kg of C is produced per hour? b) How many kg of product is obtained every hour if the cascade is replaced by a single 2 m3 tubular reactor with feed streams of 333 kg/h A and 111 kg/h B? Solution

Example problems: tubular reactors Example 18: Isothermal tubular reactor, gas phase reaction, no change in the number of moles Mehtane and sulphur react in gas phase at 600 °C and atmospheric pressure, yielding carbon disulphide and hydrogen sulfide. The reaction is carried out in an isothermal tubular reactor. The reaction rate of sulphur can be described with the equation k·cA·cB (k = 119,8 m3/mol·h), provided that the reaction equation is the following: CH4+2S2→CS2+2H2S i.e. A+2B→C+2D The feed is stoichiometric, the feed rate of methane is 23,8 mol/h. What is the required residence time to achieve an 18% conversion of methane? What is the required size of the reactor? Example 19: Isothermal, gas phase reaction, no change in the number of moles The following second-order reaction is carried out in an isothermal, ideal tubular reactor. A+BC+D

k = 5.2710-3 m3mol-1s-1

The feed contains only reactants. The pressure and temperature in the reactor are 1.3 bar and 500 °C. a) The feed stream contains the component is stoichiometric ratio. What percent conversion can be achieved with a residence time of 8 s?? b) What is the required residence time if twice the required amount of component A is added, and 40% percent conversion is desired? What percent is the flow rate of that in part a)?

7

L v2 t t 8s  2  1  1,46 t 2 5,47 2 s v1 L t1

Example 20: Isothermal tubular reactor, homogeneous liquid phase reaction A liquid phase reaction of the type A+B→C is to be carried out under isothermal conditions. Two 0,5 m3 ideal tubular reactors are available. The concentrations of the components in the 25 kmol/h feed stream is 20–20 kmol/m3. The reaction is second-order. At the feed temperature of 25 °C, the reaction rate constant is 0.125 m3/(kmol·h). a) What is the conversion in the reactors separately and in total, if they are in series? What is the amount of C in the outlet stream? b) What is the conversion if the two reactors are parallel and divide the feed streams equally? Solution

nc  8,33

kmol h

X  0,33

Example 21: Isothermal first-order irreversible reaction A reaction of the type A→B, first-order with respect to A, is carried out in dilute solution in an isothermal tubular reactor. The reaction rate constant can be calculated with the Arrhenius equation and at 20 °C its value is k = 8.53 h-1. The feed concentration of component A is 0.250 mol/dm3, the feed rate is 0.35 dm3/min. E = 4752.6 J/mol. Calculate the conversion if a) the reaction is carried out at 20 °C, b) the reaction is carried out at 150 °C. Example 22: Adiabatic reaction, gas phase reaction, no change in the number of moles Carbon monoxide and water are converted into carbon dioxide and hydrogen at atmospheric pressure in an adiabatic tubular reactor. The reaction goes to equilibrium. The feed temperature is 380 °C, the feed rate 2.5 m3/s. The ratio of CO and H2O in the feed is 1:4, the feed contains no inert gas of reaction products. The outlet stream temperature is 500 °C. The reaction enthalpy is –39,4 kJ/mol, the molar heat capacity of the gas mixture is 34 kJ/(kmol·K). Calculate the conversion and the maximal temperature increase for the reaction!

8

Example 23: Adiabatic reaction, tube reactor, liquid phase second-order reaction A second-order A+B→C+D reaction is carried out in an ideal adiabatic tube reactor with a volume of 0.12 m3. The reaction rate constant can be calculated with the equation 6.52·105·e-42300/RT kmol/(m3·s). The initial concentration of both components is 1,1 kmol/m3. The feed contains no product, its temperature is 12 °C, the feed rate is 4·10-4 m3/s. The reaction enthalpy is –42600 kJ/kmol, the specific heat capacity of the mixture is 2800 J/(kg·K), its density is 840 kg/m3. Calculate the conversion! Example 24: Cooled tubular reactor The first-order reaction A→R is carried out in a tubular reactor at 50 °C. The reaction is exothermic, thus a heat exchanger is used as a reactor. The reaction mixture flows in the tubes, the coolant (water) flows in the jacket. The molar heat capacity of the reaction mixture is 33.5 kJ/(kmol·°C), the specific heat capacity of the cooling water is 4,18 kJ/(kg·°C), the initieal concentration is 0.4 kmol/m3, the reaction rate coefficient is 0.128 s-1, the feed rate is 10.2 m3/h, the overall heat transfer coefficient is 852 W/(m2·K), the reaction enthalpy is –8.32·104 kJ/kmol, the reaction mixture has a viscosity of 4,4 mPas and a density of 900 kg/m3. a) Calculate the volume for 90% conversion! b) What is the required number and length of tubes, if the inner diameter of the tubes is 2.54 cm? (Turbulent flow must be maintained in order for the overall heat transfer coefficient not to degrade.) c) Should the heat exchanger be counterflow or coflow? Reason your answer! Calculate the inlet temperature and flow rate of the cooling water! A reminder: using computed data, the logarithmic temperature difference and geometric data, the heat flow across the wall can be calculated. The wall thickness is again neglected. Let us compare the results: Tá tl 

( T  Th,be )  (T  Th,ki ) (50C  18,6C)  (50C  46,86C )  12,27C  50 C 18,6 C T  Th,b...